The Gaussian Statistical Predictability of Wind Speeds

Adam H. Monahan School of Earth and Ocean Sciences, University of Victoria, Victoria, British Columbia, Canada

Search for other papers by Adam H. Monahan in
Current site
Google Scholar
PubMed
Close
Restricted access

Abstract

The statistical predictability of wind speed using Gaussian predictors, relative to the predictability of orthogonal vector wind components, is considered. With the assumption that the vector wind components are Gaussian, analytic expressions for the correlation-based wind speed prediction skill are obtained in terms of the prediction skills of the vector wind components and their statistical moments. It is shown that

  • at least one of the vector wind components is generally better predicted than the wind speed (often much more so);

  • wind speed predictions constructed from the predictions of vector wind components are more skillful than direct wind speed predictions; and

  • the linear predictability of wind speed (relative to that of the vector wind components) decreases as the variability in the vector wind increases relative to the mean.

These idealized model results are shown to be broadly consistent with linear predictive skills assessed using observed sea surface wind from the SeaWinds scatterometer. Biases in the model predictions are shown to be related to the degree to which vector wind variations are non-Gaussian.

Corresponding author address: Adam H. Monahan, School of Earth and Ocean Sciences, University of Victoria, P.O. Box 3065 STN CSC, Victoria BC V8W 3V6, Canada. E-mail: monahana@uvic.ca

Abstract

The statistical predictability of wind speed using Gaussian predictors, relative to the predictability of orthogonal vector wind components, is considered. With the assumption that the vector wind components are Gaussian, analytic expressions for the correlation-based wind speed prediction skill are obtained in terms of the prediction skills of the vector wind components and their statistical moments. It is shown that

  • at least one of the vector wind components is generally better predicted than the wind speed (often much more so);

  • wind speed predictions constructed from the predictions of vector wind components are more skillful than direct wind speed predictions; and

  • the linear predictability of wind speed (relative to that of the vector wind components) decreases as the variability in the vector wind increases relative to the mean.

These idealized model results are shown to be broadly consistent with linear predictive skills assessed using observed sea surface wind from the SeaWinds scatterometer. Biases in the model predictions are shown to be related to the degree to which vector wind variations are non-Gaussian.

Corresponding author address: Adam H. Monahan, School of Earth and Ocean Sciences, University of Victoria, P.O. Box 3065 STN CSC, Victoria BC V8W 3V6, Canada. E-mail: monahana@uvic.ca
Save
  • Brown, B. G., R. W. Katz, and A. H. Murphy, 1984: Time series models to simulate and forecast wind speed and wind power. J. Climate Appl. Meteor., 23, 1184–1195.

    • Search Google Scholar
    • Export Citation
  • Carlin, J., and J. Haslett, 1982: The probability distribution of wind power from a dispersed array of wind turbine generators. J. Appl. Meteor., 21, 303–313.

    • Search Google Scholar
    • Export Citation
  • Carter, R. G., and R. E. Keislar, 2000: Emergency response transport forecasting using historical wind field pattern matching. J. Appl. Meteor., 39, 446–462.

    • Search Google Scholar
    • Export Citation
  • Costa, A., A. Crespo, J. Navarro, G. Lizcano, H. Madsen, and E. Feitosa, 2008: A review on the young history of the wind power short-term prediction. Renewable Sustainable Energy Rev., 12, 1725–1744.

    • Search Google Scholar
    • Export Citation
  • Culver, A. M., and A. H. Monahan, 2013: The statistical predictability of surface winds over western and central Canada. J. Climate, in press.

    • Search Google Scholar
    • Export Citation
  • Giebel, G., R. Brownsword, G. Kariniotakis, M. Denhard, and C. Draxl, 2011: The state-of-the-art in short-term prediction of wind power: A literature overview. Anemos.Plus Tech. Rep., 110 pp. [Available online at http://www.prediktor.dk//publ/GGiebelEtAl-StateOfTheArtInShortTermPrediction_ANEMOSplus_2011.pdf.]

  • Gneiting, T., L. I. Stanberry, E. P. Grimit, L. Held, and N. A. Johnson, 2008: Assessing probabilistic forecasts of multivariate quantities, with an application to ensemble predictions of surface winds. Test, 17, 211–235.

    • Search Google Scholar
    • Export Citation
  • Klausner, Z., H. Kaplan, and E. Fattal, 2009: The similar days method for predicting near surface wind vectors. Meteor. Appl., 16, 569–579.

    • Search Google Scholar
    • Export Citation
  • Kretzschmar, R., P. Eckert, D. Cattani, and F. Eggimann, 2004: Neural network classifiers for local wind prediction. J. Appl. Meteor., 43, 727–738.

    • Search Google Scholar
    • Export Citation
  • Lange, M., and U. Focken, 2005: Physical Approach to Short-Term Wind Power Prediction. Springer, 208 pp.

  • Lokas, E. L., 1998: Evolution of peaks in weakly non-linear density field and dark halo profiles. Mon. Not. Roy. Astron. Soc., 296, 491–501.

    • Search Google Scholar
    • Export Citation
  • Longuet-Higgins, M., 1964: Modified Gaussian distributions for slightly nonlinear variables. Radio Sci., 68D, 1049–1062.

  • Ma, L., L. Shiyan, J. Chuanwen, H. Liu, and Y. Zhang, 2009: A review on the forecasting of wind speed and generated power. Renewable Sustainable Energy Rev., 13, 915–920.

    • Search Google Scholar
    • Export Citation
  • Monahan, A. H., 2004: A simple model for the skewness of global sea-surface winds. J. Atmos. Sci., 61, 2037–2049.

  • Monahan, A. H., 2006: The probability distribution of sea surface wind speeds. Part I: Theory and SeaWinds observations. J. Climate, 19, 497–520.

    • Search Google Scholar
    • Export Citation
  • Monahan, A. H., 2007: Empirical models of the probability distribution of sea surface wind speeds. J. Climate, 20, 5798–5814.

  • Monahan, A. H., 2012a: Can we see the wind? Statistical downscaling of historical sea surface winds in the northeast subarctic Pacific. J. Climate, 25, 1511–1528.

    • Search Google Scholar
    • Export Citation
  • Monahan, A. H., 2012b: The temporal autocorrelation structure of sea surface winds. J. Climate, 25, 6684–6700.

  • Murphy, A. H., 1988: Skill scores based on the mean square error and their relationship to the correlation coefficient. Mon. Wea. Rev., 116, 2417–2424.

    • Search Google Scholar
    • Export Citation
  • Perry, K., 2001: SeaWinds on QuikSCAT level 3: Daily, gridded ocean wind vectors (JPL SeaWinds project). California Institute of Technology Tech. Rep. D-20335, 39 pp.

  • Pinson, P., 2012: Adaptive calibration of (u, Ï…)-wind ensemble forecasts. Quart. J. Roy. Meteor. Soc., 138, 1273–1284.

  • Schuhen, N., T. L. Thorarinsdottir, and T. Gneiting, 2012: Ensemble model output statistics for wind vectors. Mon. Wea. Rev., 140, 3204–3219.

    • Search Google Scholar
    • Export Citation
  • Silverman, B. W., 1986: Density Estimation for Statistics and Data Analysis. Chapman and Hall, 175 pp.

  • Sloughter, J. M., T. Gneiting, and A. E. Raftery, 2013: Probabilistic wind vector forecasting using ensembles and Bayesian model averaging. Mon. Wea. Rev., 141, 2107–2119.

    • Search Google Scholar
    • Export Citation
  • Soman, S., H. Zareipour, O. Malik, and P. Mandal, 2010: A review of wind power and wind speed forecasting methods with different time horizons. Proc. 42nd North American Power Symp., Arlington, TX, IEEE, doi:10.1109/NAPS.2010.5619586.

  • Sun, C., and A. H. Monahan, 2013: Statistical downscaling prediction of sea surface winds over the global ocean. J. Climate, in press.

  • Thorarinsdottir, T., and T. Gneiting, 2010: Probabilistic forecasts of wind speed: Ensemble model output statistics using heteroscedastic censored regression. J. Roy. Stat. Soc., 173A, 371–388.

    • Search Google Scholar
    • Export Citation
  • van der Kamp, D., C. Curry, and A. H. Monahan, 2012: Statistical downscaling of historical monthly mean winds over a coastal region of complex terrain. II: Predicting wind components. Climate Dyn., 38, 1301–1311.

    • Search Google Scholar
    • Export Citation
  • Wilks, D. S., 2005: Statistical Methods in the Atmospheric Sciences. 2nd ed. Academic Press, 648 pp.

  • Zhang, J., S. Chowdhury, A. Messac, and L. Castillo, 2013: A multivariate and multimodal wind distribution model. Renewable Energy, 51, 436–447.

    • Search Google Scholar
    • Export Citation
All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 1985 760 87
PDF Downloads 832 116 13